If you want to remove lines containing any whitespace (tabs, spaces), try:
string fix = Regex.Replace(original, @"^\s*$\n", string.Empty, RegexOptions.Multiline);
Edit (for @Will): The simplest solution to trim trailing newlines would be to use TrimEnd
on the resulting string, e.g.:
string fix =
Regex.Replace(original, @"^\s*$\n", string.Empty, RegexOptions.Multiline)
.TrimEnd();